Chapter 2.5, Problem 2P

Another equation that has been used to model population growth is the Gompertz equation

Where and are positive constants.

Sketch the graph of versus , find the critical points, and determine whether each is asymptotically stable or unstable.

For , determine where the graph of versus is concave up and where it is concave down

For each in , show that , as given by the Gompertz equation, is never less than , as given by the logistic equation.